TSTP Solution File: MGT054+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT054+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:22:15 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT054+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 03:05:59 EDT 2022
% 0.21/0.34 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(greater_type, type, (
% 0.21/0.44 greater: ( $i * $i ) > $o)).
% 0.21/0.44 tff(age_type, type, (
% 0.21/0.44 age: ( $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_T1_1_type, type, (
% 0.21/0.44 tptp_fun_T1_1: $i)).
% 0.21/0.44 tff(tptp_fun_X_3_type, type, (
% 0.21/0.44 tptp_fun_X_3: $i)).
% 0.21/0.44 tff(sigma_type, type, (
% 0.21/0.44 sigma: $i)).
% 0.21/0.44 tff(smaller_type, type, (
% 0.21/0.44 smaller: ( $i * $i ) > $o)).
% 0.21/0.44 tff(dissimilar_type, type, (
% 0.21/0.44 dissimilar: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_T0_2_type, type, (
% 0.21/0.44 tptp_fun_T0_2: $i)).
% 0.21/0.44 tff(is_aligned_type, type, (
% 0.21/0.44 is_aligned: ( $i * $i ) > $o)).
% 0.21/0.44 tff(organization_type, type, (
% 0.21/0.44 organization: $i > $o)).
% 0.21/0.44 tff(capability_type, type, (
% 0.21/0.44 capability: ( $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_T2_0_type, type, (
% 0.21/0.44 tptp_fun_T2_0: $i)).
% 0.21/0.44 tff(has_immunity_type, type, (
% 0.21/0.44 has_immunity: ( $i * $i ) > $o)).
% 0.21/0.44 tff(has_endowment_type, type, (
% 0.21/0.44 has_endowment: $i > $o)).
% 0.21/0.44 tff(zero_type, type, (
% 0.21/0.44 zero: $i)).
% 0.21/0.44 tff(smaller_or_equal_type, type, (
% 0.21/0.44 smaller_or_equal: ( $i * $i ) > $o)).
% 0.21/0.44 tff(hazard_of_mortality_type, type, (
% 0.21/0.44 hazard_of_mortality: ( $i * $i ) > $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl((smaller(X, Y) <=> greater(Y, X)) <=> (smaller(X, Y) <=> greater(Y, X)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X)) <=> ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X)) <=> ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(4,axiom,(![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','definition_smaller')).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.44 tff(6,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.21/0.44 inference(skolemize,[status(sab)],[5])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (smaller(X, Y) <=> greater(Y, X))) | (smaller(age(X!3, T1!1), sigma) <=> greater(sigma, age(X!3, T1!1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (smaller(age(X!3, T1!1), sigma) <=> greater(sigma, age(X!3, T1!1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.44 tff(10,assumption,(has_immunity(X!3, T2!0)), introduced(assumption)).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 ((~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))) <=> (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 ((~![X: $i, T0: $i, T1: $i, T2: $i] : ((((((organization(X) & (~has_endowment(X))) & (age(X, T0) = zero)) & smaller_or_equal(age(X, T1), sigma)) & greater(age(X, T2), sigma)) & greater(sigma, zero)) => greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))) <=> (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(13,axiom,(~![X: $i, T0: $i, T1: $i, T2: $i] : ((((((organization(X) & (~has_endowment(X))) & (age(X, T0) = zero)) & smaller_or_equal(age(X, T1), sigma)) & greater(age(X, T2), sigma)) & greater(sigma, zero)) => greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem_5')).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (~![X: $i, T0: $i, T1: $i, T2: $i] : ((~(organization(X) & (~has_endowment(X)) & (age(X, T0) = zero) & smaller_or_equal(age(X, T1), sigma) & greater(age(X, T2), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X, T2), hazard_of_mortality(X, T1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.21/0.44 tff(21,plain,(
% 0.21/0.44 ~((~(organization(X!3) & (~has_endowment(X!3)) & (age(X!3, T0!2) = zero) & smaller_or_equal(age(X!3, T1!1), sigma) & greater(age(X!3, T2!0), sigma) & greater(sigma, zero))) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[20])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 (organization(X!3) & (~has_endowment(X!3)) & (age(X!3, T0!2) = zero) & smaller_or_equal(age(X!3, T1!1), sigma) & greater(age(X!3, T2!0), sigma) & greater(sigma, zero)),
% 0.21/0.44 inference(or_elim,[status(thm)],[21])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (~has_endowment(X!3)),
% 0.21/0.44 inference(and_elim,[status(thm)],[22])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (organization(X!3)),
% 0.21/0.44 inference(and_elim,[status(thm)],[22])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (^[X: $i, T: $i] : refl(((~has_immunity(X, T)) | has_endowment(X) | (~organization(X))) <=> ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 (![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X))) <=> ![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (^[X: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & (~has_endowment(X))) <=> (~(has_endowment(X) | (~organization(X))))), ((~(organization(X) & (~has_endowment(X)))) <=> (~(~(has_endowment(X) | (~organization(X))))))), rewrite((~(~(has_endowment(X) | (~organization(X))))) <=> (has_endowment(X) | (~organization(X)))), ((~(organization(X) & (~has_endowment(X)))) <=> (has_endowment(X) | (~organization(X))))), (((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X))))) <=> ((~has_immunity(X, T)) | (has_endowment(X) | (~organization(X)))))), rewrite(((~has_immunity(X, T)) | (has_endowment(X) | (~organization(X)))) <=> ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))), (((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X))))) <=> ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (![X: $i, T: $i] : ((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X))))) <=> ![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 (![X: $i, T: $i] : ((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X))))) <=> ![X: $i, T: $i] : ((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (^[X: $i, T: $i] : rewrite(((organization(X) & (~has_endowment(X))) => (~has_immunity(X, T))) <=> ((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (![X: $i, T: $i] : ((organization(X) & (~has_endowment(X))) => (~has_immunity(X, T))) <=> ![X: $i, T: $i] : ((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.45 tff(32,axiom,(![X: $i, T: $i] : ((organization(X) & (~has_endowment(X))) => (~has_immunity(X, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption_1')).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (![X: $i, T: $i] : ((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (![X: $i, T: $i] : ((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.45 tff(35,plain,(
% 0.21/0.45 ![X: $i, T: $i] : ((~has_immunity(X, T)) | (~(organization(X) & (~has_endowment(X)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[34])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 (((~![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))) | (has_endowment(X!3) | (~organization(X!3)) | (~has_immunity(X!3, T2!0)))) <=> ((~![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))) | has_endowment(X!3) | (~organization(X!3)) | (~has_immunity(X!3, T2!0)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (((~has_immunity(X!3, T2!0)) | has_endowment(X!3) | (~organization(X!3))) <=> (has_endowment(X!3) | (~organization(X!3)) | (~has_immunity(X!3, T2!0)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (((~![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))) | ((~has_immunity(X!3, T2!0)) | has_endowment(X!3) | (~organization(X!3)))) <=> ((~![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))) | (has_endowment(X!3) | (~organization(X!3)) | (~has_immunity(X!3, T2!0))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (((~![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))) | ((~has_immunity(X!3, T2!0)) | has_endowment(X!3) | (~organization(X!3)))) <=> ((~![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))) | has_endowment(X!3) | (~organization(X!3)) | (~has_immunity(X!3, T2!0)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[40, 38])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 ((~![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))) | ((~has_immunity(X!3, T2!0)) | has_endowment(X!3) | (~organization(X!3)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 ((~![X: $i, T: $i] : ((~has_immunity(X, T)) | has_endowment(X) | (~organization(X)))) | has_endowment(X!3) | (~organization(X!3)) | (~has_immunity(X!3, T2!0))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[43, 37, 24, 23, 10])).
% 0.21/0.45 tff(45,plain,(~has_immunity(X!3, T2!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(46,assumption,(greater(capability(X!3, T1!1), capability(X!3, T2!0))), introduced(assumption)).
% 0.21/0.45 tff(47,assumption,(~has_immunity(X!3, T2!0)), introduced(assumption)).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 (~greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1))),
% 0.21/0.45 inference(or_elim,[status(thm)],[21])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 (^[X: $i, T0: $i, T: $i] : refl((greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X))) <=> (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X))) <=> ![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & has_immunity(X, T0) & (~has_immunity(X, T))) <=> (~((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)))), ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) <=> (~(~((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)))))), rewrite((~(~((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)))) <=> ((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T))), ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) <=> ((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)))), (((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> (((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))))), rewrite((((~organization(X)) | (~has_immunity(X, T0)) | has_immunity(X, T)) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))), (((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(rewrite(((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) <=> (organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))), ((((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ((organization(X) & has_immunity(X, T0) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))))), rewrite(((organization(X) & has_immunity(X, T0) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))), ((((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : (((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.45 tff(56,axiom,(![X: $i, T0: $i, T: $i] : (((organization(X) & has_immunity(X, T0)) & (~has_immunity(X, T))) => greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption_3')).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.21/0.45 tff(59,plain,(
% 0.21/0.45 ![X: $i, T0: $i, T: $i] : ((~(organization(X) & has_immunity(X, T0) & (~has_immunity(X, T)))) | greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[58])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (((~![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))) | (greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | (~has_immunity(X!3, T1!1)) | (~organization(X!3)))) <=> ((~![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | (~has_immunity(X!3, T1!1)) | (~organization(X!3)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 ((~![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))) | (greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | (~has_immunity(X!3, T1!1)) | (~organization(X!3)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 ((~![X: $i, T0: $i, T: $i] : (greater(hazard_of_mortality(X, T), hazard_of_mortality(X, T0)) | has_immunity(X, T) | (~has_immunity(X, T0)) | (~organization(X)))) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | (~has_immunity(X!3, T1!1)) | (~organization(X!3))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (has_immunity(X!3, T2!0) | (~has_immunity(X!3, T1!1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[64, 61, 24, 48])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (~has_immunity(X!3, T1!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[65, 47])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (^[X: $i, T0: $i, T: $i] : refl((has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))) <=> (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))) <=> ![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0))) <=> (~(has_immunity(X, T) | has_immunity(X, T0) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))))), ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) <=> (~(~(has_immunity(X, T) | has_immunity(X, T0) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))))))), rewrite((~(~(has_immunity(X, T) | has_immunity(X, T0) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))))) <=> (has_immunity(X, T) | has_immunity(X, T0) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))), ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) <=> (has_immunity(X, T) | has_immunity(X, T0) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))))), (((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> ((has_immunity(X, T) | has_immunity(X, T0) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))))), rewrite(((has_immunity(X, T) | has_immunity(X, T0) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))), (((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> ![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((organization(X) & (~has_immunity(X, T0))) & (~has_immunity(X, T))) <=> (organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)))), ((((organization(X) & (~has_immunity(X, T0))) & (~has_immunity(X, T))) & greater(capability(X, T), capability(X, T0))) <=> ((organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T))) & greater(capability(X, T), capability(X, T0))))), rewrite(((organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T))) & greater(capability(X, T), capability(X, T0))) <=> (organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))), ((((organization(X) & (~has_immunity(X, T0))) & (~has_immunity(X, T))) & greater(capability(X, T), capability(X, T0))) <=> (organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0))))), (((((organization(X) & (~has_immunity(X, T0))) & (~has_immunity(X, T))) & greater(capability(X, T), capability(X, T0))) => greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> ((organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0))) => greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))))), rewrite(((organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0))) => greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)))), (((((organization(X) & (~has_immunity(X, T0))) & (~has_immunity(X, T))) & greater(capability(X, T), capability(X, T0))) => greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((((organization(X) & (~has_immunity(X, T0))) & (~has_immunity(X, T))) & greater(capability(X, T), capability(X, T0))) => greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.45 tff(74,axiom,(![X: $i, T0: $i, T: $i] : ((((organization(X) & (~has_immunity(X, T0))) & (~has_immunity(X, T))) & greater(capability(X, T), capability(X, T0))) => greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption_16')).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.21/0.45 tff(77,plain,(
% 0.21/0.45 ![X: $i, T0: $i, T: $i] : ((~(organization(X) & (~has_immunity(X, T0)) & (~has_immunity(X, T)) & greater(capability(X, T), capability(X, T0)))) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[76])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))) | (greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | has_immunity(X!3, T1!1) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0))))) <=> ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | has_immunity(X!3, T1!1) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 ((has_immunity(X!3, T1!1) | has_immunity(X!3, T2!0) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0)))) <=> (greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | has_immunity(X!3, T1!1) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))) | (has_immunity(X!3, T1!1) | has_immunity(X!3, T2!0) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0))))) <=> ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))) | (greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | has_immunity(X!3, T1!1) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))) | (has_immunity(X!3, T1!1) | has_immunity(X!3, T2!0) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0))))) <=> ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | has_immunity(X!3, T1!1) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[82, 80])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))) | (has_immunity(X!3, T1!1) | has_immunity(X!3, T2!0) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 ((~![X: $i, T0: $i, T: $i] : (has_immunity(X, T) | has_immunity(X, T0) | greater(hazard_of_mortality(X, T0), hazard_of_mortality(X, T)) | (~organization(X)) | (~greater(capability(X, T), capability(X, T0))))) | greater(hazard_of_mortality(X!3, T2!0), hazard_of_mortality(X!3, T1!1)) | has_immunity(X!3, T2!0) | has_immunity(X!3, T1!1) | (~organization(X!3)) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (has_immunity(X!3, T2!0) | has_immunity(X!3, T1!1) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[85, 79, 24, 48])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[86, 66, 47, 46])).
% 0.21/0.46 tff(88,plain,(has_immunity(X!3, T2!0) | (~greater(capability(X!3, T1!1), capability(X!3, T2!0)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 (~greater(capability(X!3, T1!1), capability(X!3, T2!0))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[88, 45])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (^[X: $i, T0: $i, T: $i] : refl((dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T))))) <=> (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T))))) <=> ![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (^[X: $i, T0: $i, T: $i] : rewrite((dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T)))) <=> (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T)))) <=> ![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[92])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T)))) <=> ![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (^[X: $i, T0: $i, T: $i] : rewrite((dissimilar(X, T0, T) <=> (organization(X) & (~(is_aligned(X, T0) <=> is_aligned(X, T))))) <=> (dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & (~(is_aligned(X, T0) <=> is_aligned(X, T))))) <=> ![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.46 tff(97,axiom,(![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & (~(is_aligned(X, T0) <=> is_aligned(X, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','definition_2')).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.21/0.46 tff(100,plain,(
% 0.21/0.46 ![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (organization(X) & ((~is_aligned(X, T0)) <=> is_aligned(X, T))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[99])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 ((~![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T)))))) | (dissimilar(X!3, T0!2, T2!0) <=> (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (dissimilar(X!3, T0!2, T2!0) <=> (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (age(X!3, T0!2) = zero),
% 0.21/0.46 inference(and_elim,[status(thm)],[22])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (^[X: $i, T0: $i, T: $i] : refl(((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero))) <=> ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero))) <=> ![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & (age(X, T0) = zero)) <=> (~((~organization(X)) | (~(age(X, T0) = zero))))), ((~(organization(X) & (age(X, T0) = zero))) <=> (~(~((~organization(X)) | (~(age(X, T0) = zero))))))), rewrite((~(~((~organization(X)) | (~(age(X, T0) = zero))))) <=> ((~organization(X)) | (~(age(X, T0) = zero)))), ((~(organization(X) & (age(X, T0) = zero))) <=> ((~organization(X)) | (~(age(X, T0) = zero))))), (((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))) <=> (((~organization(X)) | (~(age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))))), rewrite((((~organization(X)) | (~(age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))) <=> ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))), (((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))) <=> ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))) <=> ![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (^[X: $i, T0: $i, T: $i] : rewrite(((organization(X) & (age(X, T0) = zero)) => (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))) <=> ((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : ((organization(X) & (age(X, T0) = zero)) => (greater(age(X, T), sigma) <=> dissimilar(X, T0, T))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.46 tff(113,axiom,(![X: $i, T0: $i, T: $i] : ((organization(X) & (age(X, T0) = zero)) => (greater(age(X, T), sigma) <=> dissimilar(X, T0, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption_15')).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.21/0.46 tff(116,plain,(
% 0.21/0.46 ![X: $i, T0: $i, T: $i] : ((~(organization(X) & (age(X, T0) = zero))) | (greater(age(X, T), sigma) <=> dissimilar(X, T0, T)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[115])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.21/0.46 tff(118,plain,
% 0.21/0.46 (![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[117, 107])).
% 0.21/0.46 tff(119,plain,
% 0.21/0.46 (((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)))) <=> ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 (((greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero))) <=> ((~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 (((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))) <=> ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.46 tff(122,plain,
% 0.21/0.46 (((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))) <=> ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[121, 119])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.46 tff(125,plain,
% 0.21/0.46 (greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[124, 118, 24, 105])).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 (greater(age(X!3, T2!0), sigma)),
% 0.21/0.46 inference(and_elim,[status(thm)],[22])).
% 0.21/0.46 tff(127,plain,
% 0.21/0.46 ((~(greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0))) | (~greater(age(X!3, T2!0), sigma)) | dissimilar(X!3, T0!2, T2!0)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(128,plain,
% 0.21/0.46 ((~(greater(age(X!3, T2!0), sigma) <=> dissimilar(X!3, T0!2, T2!0))) | dissimilar(X!3, T0!2, T2!0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 (dissimilar(X!3, T0!2, T2!0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 ((~(dissimilar(X!3, T0!2, T2!0) <=> (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0)))))) | (~dissimilar(X!3, T0!2, T2!0)) | (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 ((~(dissimilar(X!3, T0!2, T2!0) <=> (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0)))))) | (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[131, 104])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0))) | (~(is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (~(is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (^[X: $i, T: $i] : refl((is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero))) <=> (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero))) <=> ![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (^[X: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & (age(X, T) = zero)) <=> (~((~organization(X)) | (~(age(X, T) = zero))))), ((~(organization(X) & (age(X, T) = zero))) <=> (~(~((~organization(X)) | (~(age(X, T) = zero))))))), rewrite((~(~((~organization(X)) | (~(age(X, T) = zero))))) <=> ((~organization(X)) | (~(age(X, T) = zero)))), ((~(organization(X) & (age(X, T) = zero))) <=> ((~organization(X)) | (~(age(X, T) = zero))))), (((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T)) <=> (((~organization(X)) | (~(age(X, T) = zero))) | is_aligned(X, T)))), rewrite((((~organization(X)) | (~(age(X, T) = zero))) | is_aligned(X, T)) <=> (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))), (((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T)) <=> (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (![X: $i, T: $i] : ((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T)) <=> ![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (![X: $i, T: $i] : ((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T)) <=> ![X: $i, T: $i] : ((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (^[X: $i, T: $i] : rewrite(((organization(X) & (age(X, T) = zero)) => is_aligned(X, T)) <=> ((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (![X: $i, T: $i] : ((organization(X) & (age(X, T) = zero)) => is_aligned(X, T)) <=> ![X: $i, T: $i] : ((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[140])).
% 0.21/0.47 tff(142,axiom,(![X: $i, T: $i] : ((organization(X) & (age(X, T) = zero)) => is_aligned(X, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption_13')).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (![X: $i, T: $i] : ((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 (![X: $i, T: $i] : ((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.21/0.47 tff(145,plain,(
% 0.21/0.47 ![X: $i, T: $i] : ((~(organization(X) & (age(X, T) = zero))) | is_aligned(X, T))),
% 0.21/0.47 inference(skolemize,[status(sab)],[144])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 (![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 (![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[146, 136])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (((~![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))) | ((~organization(X!3)) | is_aligned(X!3, T0!2) | (~(age(X!3, T0!2) = zero)))) <=> ((~![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))) | (~organization(X!3)) | is_aligned(X!3, T0!2) | (~(age(X!3, T0!2) = zero)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 ((is_aligned(X!3, T0!2) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero))) <=> ((~organization(X!3)) | is_aligned(X!3, T0!2) | (~(age(X!3, T0!2) = zero)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 (((~![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))) | (is_aligned(X!3, T0!2) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))) <=> ((~![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))) | ((~organization(X!3)) | is_aligned(X!3, T0!2) | (~(age(X!3, T0!2) = zero))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[149])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (((~![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))) | (is_aligned(X!3, T0!2) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))) <=> ((~![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))) | (~organization(X!3)) | is_aligned(X!3, T0!2) | (~(age(X!3, T0!2) = zero)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[150, 148])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 ((~![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))) | (is_aligned(X!3, T0!2) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 ((~![X: $i, T: $i] : (is_aligned(X, T) | (~organization(X)) | (~(age(X, T) = zero)))) | (~organization(X!3)) | is_aligned(X!3, T0!2) | (~(age(X!3, T0!2) = zero))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.47 tff(154,plain,
% 0.21/0.47 (is_aligned(X!3, T0!2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[153, 147, 24, 105])).
% 0.21/0.47 tff(155,plain,
% 0.21/0.47 ((is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0)) | (~is_aligned(X!3, T0!2)) | (~is_aligned(X!3, T2!0))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(156,plain,
% 0.21/0.47 ((is_aligned(X!3, T0!2) <=> is_aligned(X!3, T2!0)) | (~is_aligned(X!3, T2!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.21/0.47 tff(157,plain,
% 0.21/0.47 (~is_aligned(X!3, T2!0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[156, 134])).
% 0.21/0.47 tff(158,assumption,(is_aligned(X!3, T1!1)), introduced(assumption)).
% 0.21/0.47 tff(159,assumption,(~greater(capability(X!3, T1!1), capability(X!3, T2!0))), introduced(assumption)).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 (^[X: $i, T0: $i, T: $i] : refl((is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X))) <=> (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 (![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X))) <=> ![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[160])).
% 0.21/0.47 tff(162,plain,
% 0.21/0.47 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((organization(X) & is_aligned(X, T0) & (~is_aligned(X, T))) <=> (~((~organization(X)) | (~is_aligned(X, T0)) | is_aligned(X, T)))), ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) <=> (~(~((~organization(X)) | (~is_aligned(X, T0)) | is_aligned(X, T)))))), rewrite((~(~((~organization(X)) | (~is_aligned(X, T0)) | is_aligned(X, T)))) <=> ((~organization(X)) | (~is_aligned(X, T0)) | is_aligned(X, T))), ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) <=> ((~organization(X)) | (~is_aligned(X, T0)) | is_aligned(X, T)))), (((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T))) <=> (((~organization(X)) | (~is_aligned(X, T0)) | is_aligned(X, T)) | greater(capability(X, T0), capability(X, T))))), rewrite((((~organization(X)) | (~is_aligned(X, T0)) | is_aligned(X, T)) | greater(capability(X, T0), capability(X, T))) <=> (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))), (((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T))) <=> (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(163,plain,
% 0.21/0.47 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T))) <=> ![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[162])).
% 0.21/0.47 tff(164,plain,
% 0.21/0.47 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 (^[X: $i, T0: $i, T: $i] : trans(monotonicity(rewrite(((organization(X) & is_aligned(X, T0)) & (~is_aligned(X, T))) <=> (organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))), ((((organization(X) & is_aligned(X, T0)) & (~is_aligned(X, T))) => greater(capability(X, T0), capability(X, T))) <=> ((organization(X) & is_aligned(X, T0) & (~is_aligned(X, T))) => greater(capability(X, T0), capability(X, T))))), rewrite(((organization(X) & is_aligned(X, T0) & (~is_aligned(X, T))) => greater(capability(X, T0), capability(X, T))) <=> ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T)))), ((((organization(X) & is_aligned(X, T0)) & (~is_aligned(X, T))) => greater(capability(X, T0), capability(X, T))) <=> ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(166,plain,
% 0.21/0.47 (![X: $i, T0: $i, T: $i] : (((organization(X) & is_aligned(X, T0)) & (~is_aligned(X, T))) => greater(capability(X, T0), capability(X, T))) <=> ![X: $i, T0: $i, T: $i] : ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[165])).
% 0.21/0.47 tff(167,axiom,(![X: $i, T0: $i, T: $i] : (((organization(X) & is_aligned(X, T0)) & (~is_aligned(X, T))) => greater(capability(X, T0), capability(X, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption_14')).
% 0.21/0.47 tff(168,plain,
% 0.21/0.47 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.47 tff(169,plain,
% 0.21/0.47 (![X: $i, T0: $i, T: $i] : ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.21/0.47 tff(170,plain,(
% 0.21/0.47 ![X: $i, T0: $i, T: $i] : ((~(organization(X) & is_aligned(X, T0) & (~is_aligned(X, T)))) | greater(capability(X, T0), capability(X, T)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[169])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 (![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 (![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 (((~![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))) | ((~organization(X!3)) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | is_aligned(X!3, T2!0) | (~is_aligned(X!3, T1!1)))) <=> ((~![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))) | (~organization(X!3)) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | is_aligned(X!3, T2!0) | (~is_aligned(X!3, T1!1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 ((is_aligned(X!3, T2!0) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | (~is_aligned(X!3, T1!1)) | (~organization(X!3))) <=> ((~organization(X!3)) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | is_aligned(X!3, T2!0) | (~is_aligned(X!3, T1!1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(175,plain,
% 0.21/0.48 (((~![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))) | (is_aligned(X!3, T2!0) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | (~is_aligned(X!3, T1!1)) | (~organization(X!3)))) <=> ((~![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))) | ((~organization(X!3)) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | is_aligned(X!3, T2!0) | (~is_aligned(X!3, T1!1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[174])).
% 0.21/0.48 tff(176,plain,
% 0.21/0.48 (((~![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))) | (is_aligned(X!3, T2!0) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | (~is_aligned(X!3, T1!1)) | (~organization(X!3)))) <=> ((~![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))) | (~organization(X!3)) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | is_aligned(X!3, T2!0) | (~is_aligned(X!3, T1!1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[175, 173])).
% 0.21/0.48 tff(177,plain,
% 0.21/0.48 ((~![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))) | (is_aligned(X!3, T2!0) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | (~is_aligned(X!3, T1!1)) | (~organization(X!3)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 ((~![X: $i, T0: $i, T: $i] : (is_aligned(X, T) | greater(capability(X, T0), capability(X, T)) | (~is_aligned(X, T0)) | (~organization(X)))) | (~organization(X!3)) | greater(capability(X!3, T1!1), capability(X!3, T2!0)) | is_aligned(X!3, T2!0) | (~is_aligned(X!3, T1!1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.21/0.48 tff(179,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[178, 172, 24, 159, 158, 157])).
% 0.21/0.48 tff(180,plain,(greater(capability(X!3, T1!1), capability(X!3, T2!0)) | (~is_aligned(X!3, T1!1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 (~is_aligned(X!3, T1!1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[180, 89])).
% 0.21/0.48 tff(182,plain,
% 0.21/0.48 ((~(is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1))) | (~is_aligned(X!3, T0!2)) | is_aligned(X!3, T1!1)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 ((~(is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1))) | is_aligned(X!3, T1!1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[182, 154])).
% 0.21/0.48 tff(184,plain,
% 0.21/0.48 (~(is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[183, 181])).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 ((~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1)))) | (~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 ((~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1)))) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[185, 24])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[186, 184])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 ((~![X: $i, T0: $i, T: $i] : (dissimilar(X, T0, T) <=> (~((~organization(X)) | (is_aligned(X, T0) <=> is_aligned(X, T)))))) | (dissimilar(X!3, T0!2, T1!1) <=> (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 (dissimilar(X!3, T0!2, T1!1) <=> (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[188, 102])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 ((~(dissimilar(X!3, T0!2, T1!1) <=> (~((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1)))))) | dissimilar(X!3, T0!2, T1!1) | ((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 (dissimilar(X!3, T0!2, T1!1) | ((~organization(X!3)) | (is_aligned(X!3, T0!2) <=> is_aligned(X!3, T1!1)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (dissimilar(X!3, T0!2, T1!1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[191, 187])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 (((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)))) <=> ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 (((greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero))) <=> ((~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 (((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))) <=> ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[194])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 (((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))) <=> ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[195, 193])).
% 0.21/0.48 tff(197,plain,
% 0.21/0.48 ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | ((greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 ((~![X: $i, T0: $i, T: $i] : ((greater(age(X, T), sigma) <=> dissimilar(X, T0, T)) | (~organization(X)) | (~(age(X, T0) = zero)))) | (~organization(X!3)) | (~(age(X!3, T0!2) = zero)) | (greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 (greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[198, 118, 24, 105])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 ((~(greater(age(X!3, T1!1), sigma) <=> dissimilar(X!3, T0!2, T1!1))) | greater(age(X!3, T1!1), sigma) | (~dissimilar(X!3, T0!2, T1!1))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(201,plain,
% 0.21/0.48 (greater(age(X!3, T1!1), sigma) | (~dissimilar(X!3, T0!2, T1!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (greater(age(X!3, T1!1), sigma)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[201, 192])).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 (^[X: $i, Y: $i] : refl(((~greater(X, Y)) | (~greater(Y, X))) <=> ((~greater(X, Y)) | (~greater(Y, X))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X))) <=> ![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[203])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((greater(X, Y) & greater(Y, X)) <=> (~((~greater(X, Y)) | (~greater(Y, X))))), ((~(greater(X, Y) & greater(Y, X))) <=> (~(~((~greater(X, Y)) | (~greater(Y, X))))))), rewrite((~(~((~greater(X, Y)) | (~greater(Y, X))))) <=> ((~greater(X, Y)) | (~greater(Y, X)))), ((~(greater(X, Y) & greater(Y, X))) <=> ((~greater(X, Y)) | (~greater(Y, X)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X))) <=> ![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[205])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X))) <=> ![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(208,axiom,(![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','meaning_postulate_greater_strict')).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.48 tff(210,plain,(
% 0.21/0.48 ![X: $i, Y: $i] : (~(greater(X, Y) & greater(Y, X)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[209])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.21/0.48 tff(213,plain,
% 0.21/0.48 (((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | ((~greater(sigma, age(X!3, T1!1))) | (~greater(age(X!3, T1!1), sigma)))) <=> ((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | (~greater(sigma, age(X!3, T1!1))) | (~greater(age(X!3, T1!1), sigma)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 ((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | ((~greater(sigma, age(X!3, T1!1))) | (~greater(age(X!3, T1!1), sigma)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(215,plain,
% 0.21/0.48 ((~![X: $i, Y: $i] : ((~greater(X, Y)) | (~greater(Y, X)))) | (~greater(sigma, age(X!3, T1!1))) | (~greater(age(X!3, T1!1), sigma))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.48 tff(216,plain,
% 0.21/0.48 ((~greater(sigma, age(X!3, T1!1))) | (~greater(age(X!3, T1!1), sigma))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[215, 212])).
% 0.21/0.48 tff(217,plain,
% 0.21/0.48 (~greater(sigma, age(X!3, T1!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[216, 202])).
% 0.21/0.48 tff(218,plain,
% 0.21/0.48 ((~(smaller(age(X!3, T1!1), sigma) <=> greater(sigma, age(X!3, T1!1)))) | (~smaller(age(X!3, T1!1), sigma)) | greater(sigma, age(X!3, T1!1))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(219,plain,
% 0.21/0.48 ((~(smaller(age(X!3, T1!1), sigma) <=> greater(sigma, age(X!3, T1!1)))) | (~smaller(age(X!3, T1!1), sigma))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.21/0.48 tff(220,plain,
% 0.21/0.48 (~smaller(age(X!3, T1!1), sigma)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[219, 9])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 (^[X: $i, Y: $i] : refl((smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[221])).
% 0.21/0.49 tff(223,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(224,plain,
% 0.21/0.49 (^[X: $i, Y: $i] : rewrite((smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y))) <=> (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(225,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[224])).
% 0.21/0.49 tff(226,axiom,(![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> (smaller(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax','definition_smaller_or_equal')).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.21/0.49 tff(229,plain,(
% 0.21/0.49 ![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[228])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.21/0.49 tff(231,plain,
% 0.21/0.49 ((~![X: $i, Y: $i] : (smaller_or_equal(X, Y) <=> ((X = Y) | smaller(X, Y)))) | (smaller_or_equal(age(X!3, T1!1), sigma) <=> ((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 (smaller_or_equal(age(X!3, T1!1), sigma) <=> ((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (smaller_or_equal(age(X!3, T1!1), sigma)),
% 0.21/0.49 inference(and_elim,[status(thm)],[22])).
% 0.21/0.49 tff(234,plain,
% 0.21/0.49 ((~(smaller_or_equal(age(X!3, T1!1), sigma) <=> ((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma)))) | (~smaller_or_equal(age(X!3, T1!1), sigma)) | ((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 ((~(smaller_or_equal(age(X!3, T1!1), sigma) <=> ((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma)))) | ((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 ((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[235, 232])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 ((~((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma))) | (age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 ((age(X!3, T1!1) = sigma) | smaller(age(X!3, T1!1), sigma)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 (age(X!3, T1!1) = sigma),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[238, 220])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 (sigma = age(X!3, T1!1)),
% 0.21/0.49 inference(symmetry,[status(thm)],[239])).
% 0.21/0.49 tff(241,plain,
% 0.21/0.49 (greater(sigma, age(X!3, T1!1)) <=> greater(age(X!3, T1!1), sigma)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[240, 239])).
% 0.21/0.49 tff(242,plain,
% 0.21/0.49 (greater(age(X!3, T1!1), sigma) <=> greater(sigma, age(X!3, T1!1))),
% 0.21/0.49 inference(symmetry,[status(thm)],[241])).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 (greater(sigma, age(X!3, T1!1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[202, 242])).
% 0.21/0.49 tff(244,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[217, 243])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------